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Question
Find the derivative of the inverse function of the following : y = x log x
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Solution
y = x log x
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"(xlogx)`
= `x"d"/"dx"(logx) + (logx)."d"/"dx"(x)`
= `x xx 1/x + (logx) xx 1`
= 1 + logx
The derivative of inverse function of y = f(x) is given by
`"dx"/"dy" = (1)/(("dy"/"dx")`
= `(1)/(1 + logx)`.
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